In this work we provide a characterization of C^(k,1) functions on R^n (that is k times differentiable with locally Lipschitz k-th derivatives) by means of (k+1)-th divided differences and Riemann derivatives. In particular we prove that the class of C^(k,1) functions is equivalent to the class of functions with bounded (k+1)-th divided difference. From this result we deduce a Taylor's formula for this class of functions and a characterization through Riemann derivatives

A characterization of C^{K,1} functions / D. La Torre, M. Rocca. - In: REAL ANALYSIS EXCHANGE. - ISSN 0147-1937. - 27:2(2002), pp. 515-534.

A characterization of C^{K,1} functions

D. La Torre
Primo
;
2002

Abstract

In this work we provide a characterization of C^(k,1) functions on R^n (that is k times differentiable with locally Lipschitz k-th derivatives) by means of (k+1)-th divided differences and Riemann derivatives. In particular we prove that the class of C^(k,1) functions is equivalent to the class of functions with bounded (k+1)-th divided difference. From this result we deduce a Taylor's formula for this class of functions and a characterization through Riemann derivatives
Characterization of C^(k,1) functions ; Riemann derivatives ; Taylor's formula
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
http://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID616608_code414528.pdf?abstractid=616608&mirid=1
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/179211
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